DSE Past Paper (Modified)

$ \mbox{If } \dfrac{a}{x} + \dfrac{b}{y} = 2, \mbox{ then } x = $

In the figure, $ \, {ABCD} \, $ is a parallelogram. $E \,$ is a point lying on $\,CD\,$ such that $\ BE=CE\, .$
If $\ \angle ADC=120°, \ $ then $\ \angle ABE= $

According to the figure, which of the following must be true?

$ \begin{array}{ll}\textrm{I.} & a + c = b \\
\textrm{II.} &a + b = 180° + c \\
\textrm{III.} &b + c =3 60° \end{array} $

In the figure, the 1st pattern consists of 11 dots.
For any positive integer $n\,$, the $\,(n+1)$th pattern is
formed by adding 6 dots to the $\,n$-th pattern.
Find the number of dots in the 7th pattern.

If  $ x \mbox{ and } \  y$ are non-zero numbers such that
$\ (4y – 3x):(2x + y) = 5:6, \, $ then $\ x:y= $

The monthly salary of Danny is \( 25\%\,\) higher than that of Paul while
the monthly salary of Paul is \(\ 25\%\, \) lower than that of Tracy.
It is given that the monthly salary of Donald is \(\ $37\,800 \, . \)
The monthly salary of Tracy is:

If $ –2 \lt a \lt 0 $, which of the following may represent the graph of $ y=(ax+2)^2+a \; ?$

If \(\ k \) is a constant such that the quadratic equation \(\ x^2+kx + 6k + 64 = 0 \ \) has equal roots, then \(\ k =\)

Let $ f(x) = 8x^3 + kx + 2 \;, $   where $ k $ is a constant.   If $f(x) \, $ is divisible by $ 2x+1,$   find the remainder when $ f(x) \ $ is divided by $x + 1.$

\( 0.0865423 = \)

\( 25 – (2x-3y)^2 = \)

$ 27^{222} \cdot 5^{666} = $

$ \mbox{If } \: 3\alpha + \beta = 7\alpha + 3\beta = 4 \mbox {, find } \: \beta. $

The solution of $ \ {-7x} \gt 20 – 2x \ $   and $ \ 6x – 18 \lt 0 \ $   is